Sorting using combinational circuit, Computer Networking

Assignment Help:

Now, let us suppose a famous sequence called as bitonic sequence and sort out the elements using a combinational circuit consisting of a set of comparators. The property of bitonic sequence is as follows:

Consider a series X= x0, x1, x2, x3, x4 ................... xn-1 such that condition 1:either x0, x1, x2, x3, x4 ................... xi is a monotonically increasing sequence and xi+1, xi+2,  ................... xn-1  is a monotonically decreasing sequence or condition 2: there exists a cyclic shift of the series  x0, x1, x2, x3, x4 ................... xn-1 such that the resulting series satisfies the condition 1.

Let us take a few examples of bitonic series: B1= 4,7,8,9,11,6,3,2,1 is bitonic series

B2= 12,15,17,18,19,11,8,7,6,4,5 is bitonic series

In order to give a solution to such a bitonic sequence, various phases of comparators are needed. The basic approach followed for solving such a difficulty is as given:

 Let us say we have a bitonic series X= x0, x1, x2, x3, x4 ................... xn-1 with the property that first n/2 elements are monotonically increasing elements are monotonically increasing like x0< x1< x2< x3< x4 ... xn/2+1> ...>xn-1.  After that, these patterns are compared with the help of a comparator as follows:

Y= min(x0, xn/2), min(x1, xn/2+1), min(x2, xn/2+2), ............. Min (xn/2-1, xn-1)

Z= max(x0, xn/2), max (x1, xn/2+1), max (x2, xn/2+2), ............. max (xn/2-1, xn-1)

After the above discussed iteration, the two new bitonic series are produced and the method is called as bitonic split. After that, a recursive operation on these two bitonic sequences is processed until we are able to achieve the sorted list of elements. The exact algorithm for sorting the bitonic series is as follows:

Sort_Bitonic (X)

// Input: N Numbers following the bitonic property

// Output: Sorted List of numbers

1) The Sequence, i.e. X is transmitted on the input lines of the combinational circuit which consists of a variety of set of comparators.

2) The sequence X is divided into two sub-bitonic series say, Y and Z, with the help of a method known as bitonic split.

3) Recursively implements the bitonic split on the sub series, i.e. Y and Z, until the size

Of subsequence reaches to a level of 1.

1) The sorted series is achieved after this level on the output lines.

With the help of a diagram to demonstrate the concept of sorting using the comparators.

Example 1: Consider a unsorted list having the element values as

{3,5,8,9,10,12,14,20,95,90,60,40,35,23,18,0}

List is to be sorted in ascending order. To sort this list, in the first stage comparators of order 2 (i.e. having 2 input and 2 output) will be used. Similarly, 2nd stage will consist of 4, input comparators, 3rd stage 8 input comparator and 4th stage a 16 input comparator.

Let us consider an example with the help of a diagram to illustrate the concept of sorting using the comparators.

1875_Sorting using Combinational Circuit.png

                                                          Sorting using Combinational Circuit


Related Discussions:- Sorting using combinational circuit

Operating system for clients, Operating system for Clients All of the ...

Operating system for Clients All of the clients running popular operating systems such as Microsoft Windows, Mac OS, UNIX, etc., could be used to function as backbone software

Html, Write an HTML program segment that contains hypertext links from one ...

Write an HTML program segment that contains hypertext links from one document to another.

Difference between latches and flip flops, What is the basic difference bet...

What is the basic difference between latches and flip flops? Ans) flip flops have clock signal whereas latches dont require anyclock pulse..

Describe the sequence of events occur in host attempt, The following inform...

The following information was obtained from a host: IP address...............205.133.127.8/24 Default Gateway...... 205.133.127.1 DNS Server.............139.100.110.10

Reference models - fundamentals of networks, Reference models Design...

Reference models Designing  implementing and  manufacturing  computer  networks  and related  devices  are very  complex  activities. Therefore in order  for this  technolog

Explain the uses of firewall in computer, Explain the uses of Firewall in c...

Explain the uses of Firewall in computer For Intranet developers, restricting access of unauthorised users to the Web site has been the greatest challenge. In addition to preve

Network layer - computer network, Network Layer The  internet  network...

Network Layer The  internet  network  layer is  responsible  for moving  network  layer  packets  known data grams  from one host to another. The internet transport  layer pro

What is man, What is MAN? MAN - Metropolitan Area Networks. MAN is b...

What is MAN? MAN - Metropolitan Area Networks. MAN is bigger than a LAN and as its name implies, covers the area of a single city. MANs rarely extend beyond 100 KM and frequ

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd